The following is disclosed as a control device for continuously variable transmission in JP2004-183854A. When there is a request for kickdown acceleration, a down-shift transmission characteristic and an up-shift transmission characteristic are respectively determined based on an accelerator pedal opening and a vehicle speed and a down-shift target speed ratio suppressed more than a normal target speed ratio and an up-shift target speed ratio are calculated based on these transmission characteristics. After down-shifting to the down-shift target speed ratio, a transmission control is executed along a virtual transmission line to be shifted up according to the up-shift target speed ratio. At this time, a transmission line at the time of acceleration is set according to an acceleration start vehicle speed. The speed ratio is set to be reduced with an increase in the acceleration start vehicle speed if the accelerator pedal opening is equal. The speed ratio is set in this way in order to prevent the occurrence of so-called rubber band feel in which a drive force is not so increased as expected despite an increase in an engine rotation speed and a state as if an engine would idle is entered to give a sense of incongruity to a driver.